This is why I said I expected people to try to refute P4 — khaled

If the conclusion is that, for any given conclusion that is not self-contradictory, we can always adopt some premises from which it can be deduced, then that's just basic logic, and not subject to controversy at all. I don't see why anybody would seek to refute that. I'm not sure it would even count as philosophy.

I didn't read all the responses closely, but I didn't get the sense that anybody was silly enough to try to refute that unremarkable observation about the nature of logical systems.

That's not the conclusion yet. The conclusion is that since that is the case, any form of logic must start from an arbitrary premise for which there will never be proof, picked randomly out of an infinite set of arbitrary premises for which there will never be proof. You're actually the only one to admit this so far. Also doesn't that conclusion lead to complete nihilistic relativism? That's why people find it problematic.
Doesn't it extend to self contradictory conclusions? Because you'd have to accept the premise "Self contradictory conclusions are false" for you to say they are and there is no reason to do so.

then by modus ponens you have both 3+3=6 and 3+3 does not equal 6
— tim wood

How? By modus ponens if 2+2=7 and you replace the premises as I did accordingly in my last comment then it can be inferred that 3+3 does not equal 6 — khaled

1) If (2+2=7) then (3+3 does not equal 6)
2) If (2+2=7) then (3+3=6)

Both 1) and 2) are true.

Let both 1) an 2) stand as premises in an argument and add a third premise, 3) (2+2=7):

1) If (2+2=7) then (3+3 does not equal 6)
2) If (2+2=7) then (3+3=6)
3) (2+2=7)
----------------------------------------------
c) (3+3=6) and (3+3 does not equal 6)

You tell me what the problem is.

Truth in the meaningful sense is not the same as truth in the logical sense. Something can be logically valid but meaningfully false. Establishing truth in the meaningful sense is not the purpose of logic.

Doesn't it extend to self contradictory conclusions? Because you'd have to accept the premise "Self contradictory conclusions are false" for you to say they are and there is no reason to do so. — khaled

'False' is a concept of semantics, not logic. We need to be clear whether we're discussing logic or semantics. Semantics is about interpretations of logic, and is not logic itself.

An analog in logic to your statement "Self contradictory conclusions are false" would be the Rule of Inference that exists in Classical Logic, either as a rule of inference (eg in Natural Deduction the rule is Proof by Contradiction) or implicit from other rules (eg in a Hilbert System).

If one doesn't want to use that rule, one needs to use another form of logic. I think that's what Intuitionist Logic is.

Alternatively, one can explore Paraconsistent Logics, as Graham Priest does.

Essentially, accepting (the logical equivalent of) your statement "Self contradictory conclusions are false" is simply a choice of type of logic.

The price paid to use those other logics is that they have much less power than Classical Logic, and cannot prove many things that people intuitively feel very strongly to be the case.

Naturally there can be no logical basis on which to make that choice, as the decision is pre-logical. We cannot use logic to decide which logic to use because we haven't yet got a logic to use.

But there is a reason we accept the statement in the sense of an explanation, rather than a logical proof. That explanation is that we cannot do otherwise. We are creatures that evolved to accept that statement and we cannot successfully go against our intrinsic nature.

The reason we accept it is that, like Martin Luther, we cannot do otherwise (Ich kann nicht anders).

I agree with everything you just said but I want to know how that doesn't lead to nihilisitic relativism. That's the real problem most people have with this argument. Since there are pre logical decisions then, technically speaking, one is not "wrong" for using different logics since what defines "wrong" is not defined yet, it's just that they're unintuitive and have little predictive nature but that still doesn't make them wrong. We both seem to have no problem tying logic to purely pragmatic justifications but other people seem to staunchly reject that conclusion (See post: Where does logic get it's power). The original title of this post was "On nihilisitic relativism" but I decided to go with something a bit less clickbaity. Do you happen to be a nihilisitic relativist?

1) If (2+2=7) then (3+3 does not equal 6)
2) If (2+2=7) then (3+3=6) — tim wood

That. Where did you get that 2 was true

Do you happen to be a nihilisitic relativist? — khaled

I am a relativist in most things, but not a nihilist.

For me the difference is that both relativists and nihilists agree that there is no absolute standard whereby the truth or the value of something can be determined. But the nihilist adopts a worldview whereby they decide that nothing is true for them and nothing has value for them. The non-nihilistic relativist accepts things as being of true and of value for them, but do not insist that they must be true and of value for everybody else. Of course in practice we can observe that most things that are accepted as true and of value for one of us seem to be true and of value for most of us, because the similarities of humans are vastly greater than their differences. But that's just an observation, not a deduction.

A good example of non-nihilistic relativism is in Tim Minchin's song "If I didn't Have you (I'd probably have somebody else)". He loves his partner not because he thinks she's the smartest, most beautiful, sexiest, funniest, kindest woman on the planet, but in spite of the fact that she isn't. He loves her because she's his partner, and because she loves him.

Another example is a thoughtful, passionate fan of a football team. An example in Australia is a public intellectual Waleed Aly, who is a devoted fan of Richmond football team. He doesn't claim they're the best, or the bravest, or the coolest team in the world, and that's not why he barracks for them so ardently. He does it because they're his team, and he can acknowledge that it makes perfect sense for other people to be just as passionate about their teams. Just as Tim Minchin reckons it's reasonable for other people to prefer their life partners to his.

Far from being a nihilist, I am passionate about my politics, my ethics, my spirituality, my worldview and my aesthetic tastes. The fact that I can respect that other people may quite reasonably have different tastes, and that I don't think that mine are in any absolute sense the 'right ones' or the 'best', in no way detracts from the passion I have for mine.

But the nihilist adopts a worldview whereby they decide that nothing is true for them and nothing has value for them. — andrewk

That's not true actually. Nihilism is the recognition that all of society's values (religion, morality, politics, trends, nationalism, etc) are all ultimately based on arbitrariness and that one is free to abandon or to adopt them. It is not an ideology that orders it's followers to be depressed and to denounce any or all of these values. Nihilism is a subset of relativism that applies to society's values, it's essentially a synonym for cultural relativism. Look up "positive nihilism"

It depends where you look it up. For instance the Oxford dictionary definition is in line with what I wrote above. But let's not debate definitions. I described my worldview. I don't regard it as nihilist and I strongly reject nihilism, as I use and understand that term. If, based on my worldview outline above, you assess that I am a nihilist according to your use and understanding of that term, that's fine. It just means we use slightly different languages. No two people in the world use exactly the same language.

That's what I thought. You are not familiar with the rules of logic for hypothetical propositions. Don't worry about it; it takes a while. #2 is true. Review it online.

Or here

if T then T > T
If F then T > T
If T then F > F
If F then F > T

Hypothetical propositions are true except when the antecedent is true and the consequent false.

One can know that the statement "there is a cup on the table" is true by virtue of knowing what the statement is talking about, and then looking to see if the cup is on the table. There is no need for one to refer to another premiss. One certainly does not need to believe anything at all about visual input. If one does not believe anything at all about visual input, then one most certainly cannot use it as a premiss. If one does not know what the statement is talking about, then one cannot believe the statement. One can know what "there is a cup on the table" is talking about, and then one can look to see. We can know that they know what the statement is saying by virtue of their looking and offering an answer one way or the other. All of this happens everyday, and it happens long before one is able to carefully consider their own thought and belief.

Referring to another premiss such as "visual input is reliable" requires thinking about one's own thought and belief. That's a metacognitive endeavor. Pre-metacognitive thought and belief come first.

One can know that some statements are true, and they can know how to tell if they are long before one is able to use them as a premiss, long before having come to terms with it, long before considering the statement in isolation as a premiss.

Thought/belief and statements thereof are long prior to logic. Logic is meant to take account of them. Your argument neglects these facts and suffers as a result.

What a hypothetical 8-year-old believes about the existence or lack thereof of a cup on a table does not stand as proof neither for nor against the premise: "Visual input is reliable". Giving me an example of someone accepting said premise and using that as proof of the premise's truth value is absurd and logically flawed. It's like me saying: "The premise "The earth is flat" has no proof" and then you rebutting by saying "So you're telling me that if a flat-earther says the earth is flat, that he does not know that statement is true?"

I said that the premise "Visual input is reliable" is based on nothing and so, upon further examination, anyone would see that it is not necessarily a true premise. Also, the fact that you had to include "average" 8-year-old suggests that this isn't even that absurd. Ask the kid later "Do you KNOW that to be true?" once or twice and they'll start to doubt. If you want to tie truth to the beliefs of 8-year-olds then go ahead but I wouldn't do that.

It is not known if it is not reasoned, which is why it doesn't take that long to convince a kid that external reality is fake if you're the parent you could do that. I mean, people can convince their kids that there is a giant bearded man in the sky that knows and sees everything they're doing so.... — khaled

Care to explain why you think that this reply is relevant to what it's supposed to be addressing?

Thought/belief and statements thereof are long prior to logic. Logic is meant to take account of them — creativesoul

Correct. But thought/belief does not equal knowledge. So no. A child doesn't know that there is a cup on the table he believes there is one. As I've said, if it is not reasoned, it is not known.

...if it is not reasoned, it is not known. — khaled

It would only follow that all knowledge is existentially dependent upon thinking about thought and belief.

you seem to define knowledge as "strong belief", I define it as "reasoned belief" that's where I think we have an issue

I haven't defined it and you're avoiding a valid objection.

Using a belief statement as a premiss requires metacognition.
Metacognition includes thinking about one's own thought and belief.
Knowing what "the cup is on the table means" is talking about does not require metacognition.

If you want to tie truth to the beliefs of 8-year-olds then go ahead but I wouldn't do that. — khaled

Denying that eight year olds have true belief is outlandish!

It is not known if it is not reasoned, which is why it doesn't take that long to convince a kid that external reality is fake if you're the parent you could do that. — khaled

Reason requires a baseline from which to reason. The baseline consists of language use which talks about the world and/or ourselves. Reason requires language use about the world and/or ourselves.

One reason parents can convince a kid of anything is because the kid trusts the parent and the kid is amidst the initial formation of his/her baseline(worldview).

There is no reason whatsoever to deny that the kid can know something simply because it's still in the beginning of it's worldview development.

There is no way for a premise to be determined true or false except relative to another premise — khaled

When a the truth-value of a premise is relative to other premises, it is not called "premise" but "conclusion".

I am not avoiding anything, you're missing a distinction between knowledge and belief. All of the examples you have cited so far are examples of beliefs. Unreasoned thoughts. I maintain that knowledge requires metacognition as you defined it and that a strong belief that does not use metacognition is nothing but that, a belief.

Knowing what "the cup is on the table means" is talking about does not require metacognition. — creativesoul

Yes but knowing what it means has no bearing on it's truth value. Yes the kid knows what "the cup is on the table" means but that doesn't mean there is a cup on the table. A flat-earther knows what "the earth is flat" means but that doesn't make the earth flat

There is no reason whatsoever to deny that the kid can know something simply because it's still in the beginning of it's worldview development — creativesoul

Knowledge, as I have defined it (a belief that stems from applying sound syllogisms) is not possessed by kids who have not reasoned their beliefs. There is every reason to deny a kid that just like there is every reason to deny a flat-earther knowledge because he/she is at the beginning of forming a world view.

Denying that eight year olds have true belief is outlandish — creativesoul

First of all, that wouldn't be enough to invalidate it. Second of all, I never denied 8 year olds have true belief I denied that they have knowledge

conclusions are used as premises

it would really help if you sent me a link or something to what I'm supposed to be looking up. I really don't see the problem here

No link, really; just general education. Try seaerching hypothetical propositions, logic of See what you come up with.

In terms of the given argument, the problems are that 2+2 does not equal 7, and 3+3=6. Valid arguments do not guarantee the truth of conclusions.

P1: 3 = 1 + 2
P2: 2 + 2= 7
P3: (a+b) + (c+d) = a+b+c+d
P4: 1+1=2

C: 3+3 =/= 6

Where is the problem here. I tried looking up what you're telling me to look up but nothing comes up that seems to invalidate the argument above

I am not avoiding anything, you're missing a distinction between knowledge and belief. All of the examples you have cited so far are examples of beliefs. Unreasoned thoughts. I maintain that knowledge requires metacognition as you defined it and that a strong belief that does not use metacognition is nothing but that, a belief. — khaled

You're either avoiding the valid objection, or you don't understand it. I'll grant sincerity. You don't understand it.

Of course I've provided you examples of belief... The distinction between belief and knowledge is irrelevant here.

I'm objecting to p3. It was written as follows...

There is no way for a premise to be determined true or false except relative to another premise. — khaled

That is false. I've offered an everyday example to the contrary. The belief statement "the cup is on the table" could be used as a premiss. There is no need to consider another premiss in order to determine whether or not "the cup is on the table" is true. All that is necessary is knowing what the statement is talking about and looking to see if the cup is on the table.

QED

Knowing what "the cup is on the table means" is talking about does not require metacognition.
— creativesoul

Yes but knowing what it means has no bearing on it's truth value. Yes the kid knows what "the cup is on the table" means but that doesn't mean there is a cup on the table. A flat-earther knows what "the earth is flat" means but that doesn't make the earth flat — khaled

Nor does it need to in either case in order for the person to have knowledge prior to thinking about their own thought and belief. Thus, your criterion for knowledge is inadequate, for it cannot account of the knowledge that you yourself have admitted to here.

In both cases, the person knows what a statement is talking about.

QED

Nor does it need to in either case in order for the person to have knowledge prior to thinking about their own thought and belief — creativesoul

I maintain that it is impossible for a person to have knowledge prior to thinking about their own thought and belief therefore both of your objections do not stand as such:

1-

Of course I've provided you examples of belief... The distinction between belief and knowledge is irrelevant here. — creativesoul

Incorrect. The distinction is not at all irrelevant, it is Central to our disagreement. Perhaps I should restate premise 3 slightly differently:

There is no way for a premise to be known true or false except relative to another premise

Does this address your issue? Or do you still not understand?

2-

Thus, your criterion for knowledge is inadequate, for it cannot account of knowledge that you yourself have admitted to here. — creativesoul

The kid knows what "there is a cup on the table" means because he accepts the premises needed for the English language. When you teach someone a language all you're teaching them is a bunch of equation premises so
"Angry" = *insert abstraction of emotional state here*
"Happy" = *insert abstraction of emotional state here*
The kid knows and accepts enough of these abstractions and as a result, knows what "there is a cup on the table" means. That does not mean he knows that there is a cup on the table unless he explicitly accepts the premise "visual input is reliable". In other words, if you still fail to understand, me saying that the kid knows what "there is a cup on the table" means does not invalidate my definition of knowledge. The kid only knows the meaning of that sentence because he explicitly accepts certain premises. My definition of knowledge is consistent with what I've classified as knowledge

I maintain that it is impossible for a person to have knowledge prior to thinking about their own thought and belief therefore both of your objections do not stand as such: — khaled

One can say something as many times as one likes. That doesn't make it true. It does make it 'maintained'...

You have no idea what you're talking about.

Your entire storyline here is chock full of self contradiction.

One can know what "the cup is on the table" means without knowing what the word "premiss" means.

Do you see how that is fatal to what you maintain?

You're all over the map. What, exactly, are you about? Your question is about the following;

1) If (2+2=7) then (3+3 does not equal 6)
2) If (2+2=7) then (3+3=6)

Both 1) and 2) are true.

Let both 1) an 2) stand as premises in an argument and add a third premise, 3) (2+2=7):

1) If (2+2=7) then (3+3 does not equal 6)
2) If (2+2=7) then (3+3=6)
3) (2+2=7)
----------------------------------------------
c) (3+3=6) and (3+3 does not equal 6)

You tell me what the problem is. — tim wood

If you have some question about this, go ahead and ask it. But you're persuading me you don''t know enough about logic to ask an intelligible question, much less understand it.

Hint: 2+2 does not equal 7